Calculus Examples

$f (x) = \frac{11}{\sqrt{1 - x^{2}}}$

Step 1

The function $F (x)$ can be found by finding the indefinite integral of the derivative $f (x)$ .

$F (x) = \int f (x) d x$

Step 2

Set up the integral to solve.

$F (x) = \int \frac{11}{\sqrt{1 - x^{2}}} d x$

Step 3

Since $11$ is constant with respect to $x$ , move $11$ out of the integral.

$11 \int \frac{1}{\sqrt{1 - x^{2}}} d x$

Step 4

Rewrite $1$ as $1^{2}$ .

$11 \int \frac{1}{\sqrt{1^{2} - x^{2}}} d x$

Step 5

The integral of $\frac{1}{\sqrt{1^{2} - x^{2}}}$ with respect to $x$ is $\arcsin (x)$

$11 (\arcsin (x) + C)$

Step 6

Simplify.

$11 \arcsin (x) + C$

Step 7

The answer is the antiderivative of the function $f (x) = \frac{11}{\sqrt{1 - x^{2}}}$ .

$F (x) =$ $11 \arcsin (x) + C$